# project euler – Problem 32

November 8, 2011
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(This article was first published on YGC » R, and kindly contributed to R-bloggers)

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.
HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.


Very similar to what I implemented in Problem 41.

?View Code RSPLUS
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  vec2num <- function(vec) { m <- length(vec) n <- sum(10^(m:1-1) * vec) return(n) }     j <- 9 p <- allPerms(j, max=prod(1:j)*j) s <- 0 for (i in 1:nrow(p)) { product <- vec2num(p[i,6:9]) if (vec2num(p[i,1:2]) * vec2num(p[i,3:5]) == product) { s <- c(s,product) } if (vec2num(p[i,1]) * vec2num(p[i,2:5]) == product) { s <- c(s,product) } }   print(sum(unique(s)))
> system.time(source("Problem32.R"))
[1] 45228
user  system elapsed
35.32    0.04   35.45